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On the space of solutions of the Hořava theory at the kinetic-conformal point

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Abstract

The nonprojectable Hořava theory at the kinetic-conformal point is defined by setting a specific value of the coupling constant of the kinetic term of the Lagrangian. This formulation has two additional second class-constraints that eliminate the extra mode. We show that the space of solutions of this theory in the Hamiltonian formalism is bigger than the space of solutions in the original Lagrangian formalism. In the Hamiltonian formalism there are certain configurations for the Lagrange multipliers that lead to solutions that cannot be found in the original Lagrangian formulation. We show specific examples in vacuum and with a source. The solution with the source has homogeneous and isotropic spatial hypersurfaces. The enhancement of the space of solutions leaves the possibility that new solutions applicable to cosmology, or to other physical systems, can be found in the Hamiltonian formalism.

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Notes

  1. In Hořava theory, the vacuum spherically symmetric solutions do not possess the uniqueness properties that they have in GR.

  2. In the case of this toy model the Eq. (2.8) for \(\sigma \) and (2.11) for A result to be the same, but even in this case the solutions for \(\sigma \) and A do not need to be the same.

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Acknowledgements

A. R. is partially supported by Grant Fondecyt No. 1161192, Chile.

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Authors and Affiliations

  1. Department of Physics, Universidad de Antofagasta, 1240000, Antofagasta, Chile

    Jorge Bellorín & Alvaro Restuccia

  2. Department of Physics, Universidad Simón Bolívar, Caracas, 1080-A, Venezuela

    Alvaro Restuccia

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  1. Jorge Bellorín
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  2. Alvaro Restuccia
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Correspondence to Jorge Bellorín.

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Bellorín, J., Restuccia, A. On the space of solutions of the Hořava theory at the kinetic-conformal point. Gen Relativ Gravit 49, 132 (2017). https://doi.org/10.1007/s10714-017-2298-4

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